The growing electrification of transportation systems is dramatically increasing the waste heat that must be dissipated from high-density power electronics. Transformative embedded heat spreading technologies must be developed in next-generation systems to enable air cooling of power semiconductors with heat fluxes exceeding 500 W/cm2 over large hotspot areas up to 1 cm2. In this study, vapor chamber heat spreaders, or thermal ground planes (TGPs), with customized wick structures are investigated as one possibility. A 10 cm × 10 cm TGP with hybrid wick, which is a blend of a biporous wick with a standard monoporous wick, was designed. The TGP was tested in combination with a straight pin fin heat sink under air jet impingement and a 1 cm2 size heat source. The experimental performance of the hybrid wick TGP was compared under the same air-cooled conditions with an off-the-shelf TGP of the same size from a commercial vendor and a TGP with a biporous wick only. The customized hybrid wick TGP exhibits ∼28% lower thermal resistance compared with a traditional commercial TGP, and the capillary limit heat flux is measured as 450 W/cm2. Technical challenges in extending this capillary limit heat flux value and TGP integration into packaged electronics are described.

Introduction

A core theme in the development of next generation compact power electronics for electrified vehicles is increased power density. Active liquid cooling is conventionally employed to effectively dissipate waste heat from high power density systems. Forced liquid cooling exhibits excellent and reliable heat transfer performance in such high heat flux (>250 W/cm2) applications. However, the cooling loop should be leak-proof, may require filtering, and involves the connection of auxiliary components, which in combination increases overall system complexity. While air cooling is considered a relatively more simple and reliable approach, it is limited to low heat transfer coefficients because of the inferior thermophysical properties of air as a fluid. Thus, to apply air cooling in high volumetric power density electronics packaging, a high-performance embedded heat spreading device as a high-to-low heat flux converter is required.

Typical heat spreading technologies include solid material heat spreaders such as copper (Cu), graphite, or diamond. Another option is a vapor chamber thermal ground plane (TGP). A vapor chamber is a sealed two-phase heat transfer device enclosing a working fluid that is evaporated upon localized heat input. This vapor is then condensed over a broader heat rejection, or condenser, surface area. The liquid condensates return to the evaporator side of the chamber by the capillary force of an inner wick structure. By absorbing energy in the form of latent heat of vaporization, a vapor chamber exhibits advantages in terms of superior heat transport (i.e., spreading) capabilities.

The importance of heat spreading for air cooling and the feasibility of air cooling for a large-area (>1 cm2) high heat flux (>1 kW/cm2) device are highlighted by considering a conduction heat transfer finite element analysis (FEA) as follows [1]. In Fig. 1(a), a center cross section image of a 100 mm × 100 mm × 3 mm thick thermally conductive heat spreader is shown. On the bottom of the heat spreader, a uniform heat flux of 1 kW/cm2 is applied over a 1 cm × 1 cm center region. A convective heat transfer coefficient, h, is then applied to the top surface of the heat spreader. For simplicity, the remaining surfaces of the heat spreader are assumed to be adiabatic. The heat spreader thermal conductivity, k, is defined as a parameter in the model. Thermal conductivity values of 400, 1000, 2000, and 5000 W/(m K) are selected to represent, respectively, Cu, graphite, and diamond solid state materials plus a high value for a TGP, per Bar-Cohen et al. [2]. At the same time, the heat transfer coefficient, h, is set as a parameter to range through moderate to aggressive forced air convection values of 62.5–1000 W/(m2 K).

Figure 1(b) shows the numerical results obtained using commercial FEA software [3]. The maximum temperature at the center of the bottom of the heat spreader is plotted versus the convective heat transfer coefficient applied to the top side of the heat spreader. To achieve maximum heat spreader temperatures, 150–200 °C, that are compatible with next generation silicon carbide power devices, aggressive air cooling should be used in combination with a heat spreader that has a thermal conductivity value approaching that of a TGP. Figure 2 shows the heat flux profile along the centerline of the top of the heat spreader for the four different materials. In this case, the heat transfer coefficient, h, is set to 750 W/(m2 K). As expected, an average heat flux value of 10 W/cm2 is obtained in all four cases. However, effective thermal conductivity is critical to decreasing the peak heat flux value, which is vital for air cooling. Observe that the TGP provides the most uniform heat flux profile with a maximum value that is within a feasible range for forced convection air cooling.

From the above introduction and numerical analysis, a need exists for low-thermal-resistance and ultrathin heat spreaders that are capable of dissipating heat fluxes larger than 500 W/cm2 from relatively large electronic device areas (∼1 cm2) [1]. Thus, the major gap for air cooling of next generation wide band-gap electronics is extremely high-performance heat spreading technology such as the TGP. As explained in Ref. [4], various research groups have been investigating the underlying wick structure necessary for the proper operation of a TGP. Table 1 provides a summary of the existing wick technologies. Very high (>1.2 kW/cm2) heat fluxes that are applied over very small areas (∼0.6 mm2) with very low superheat (<10 K) have recently emerged; see Ref. [5]. Additionally, as described in Ref. [10], moderate heat flux, ∼580 W/cm2, over a large area, ∼100 mm2, with large superheat, ∼72 K, has been studied. However, a technology gap exists in Table 1, where the cooling of both large size (∼100 mm2) and extreme heat flux (>1 kW/cm2) heat sources at low superheat (<35 K) still needs to be addressed. The supply of an adequate amount of liquid coolant to avoid dryout of the wick at the evaporator of a TGP via a 3D liquid feed structure should be considered a primary research direction [5,12]. Thus, the development of high performance two-phase thermal ground plane vapor chambers remains a critical field for further research in the context of future compact air-cooled electronics.

The current work herein applies the biporous sintered wick structure developed and tested by Semenic et al. [13] at wick level. In this work, they demonstrated the capability of the wick to spread a heat flux of 990 W/cm2 applied over a relatively large area of 0.32 cm2. Here, the same strategy is applied to a vapor chamber TGP with a spreading area of ∼10 × 10 cm2 and a heated area of 1 × 1 cm2. The heat spreading performance of the TGP is tested with an air jet impingement cooled heat sink, as a benchmark. Besides the biporous wick, a hybrid wick reported later by the same group in Ref. [14], which is a combination of a biporous wick and a standard monoporous wick, is applied to the same size TGP for experimental evaluation. The performance of the two TGPs is compared with an off-the-shelf TGP of the same size from a commercial vendor2 under the same air-cooled conditions. Most often, the performance of a TGP is tested with liquid cooling on the condenser side, and only a few publications [1518] that utilize an air-cooled system, albeit under low heat flux conditions, can be found. Hence, in this investigation, the TGP performance is tested under high heat flux conditions (produced by a large heater area) with air cooling, which is challenging. In the end, a novel two-layer wick structure, which theoretically should have improved performance, is proposed and will be applied to a TGP for future evaluation.

Vapor Chamber Wick Structures

Depending on porosity, a wick structure can be categorized as either a monoporous or a biporous structure. Low porosity monoporous structures offer larger capillary driving force for more efficient return of condensate [4]. However, the low permeability of the small-particle features prevents the vapor bubbles from penetrating through the wick readily [4]. Hence, high porosity and permeability biporous wicks with large pores are an alternative, despite their shortcoming of higher thermal resistance. A hybrid porous wick design combining monoporous and biporous features thus naturally emerged as another compromise solution. In the hybrid wick structure, a monoporous interface layer is sandwiched between the biporous material and the Cu substrate; refer to Ref. [14]. Vapor travels easily through the wick structure due to the upper biporous structure. Meanwhile, working fluid resupply benefits from the embedded monoporous layer, and at high heat flux, the top biporous wick can help local liquid supply as well.

Figure 3 shows a schematic of the monoporous wick (left), biporous wick (middle), and hybrid wick (right). The TGP with monoporous wick is a standard product from a commercial vendor, Celsia Inc. (Santa Clara, CA)2 with 60 μm Cu particles being sintered to form a θmono= 1500 μm thick wick layer. Same wick structures were applied to both the evaporator side and the condenser side of all the three TGPs.

For fair comparison, the other two TGPs have the same wick thickness and were constructed based on the specifications from this research investigation. The biporous wick was fabricated by sintering 60 μm Cu particles to form a 300 μm thick wick sheet with about five particles through the thickness. The wick sheet then was broken into pieces (clusters) and sieved with screen mesh to obtain a specific cluster size (300 μm). The combination of 60 μm Cu particles with the 300 μm cluster size originated from the results reported by Semenic et al. [9,13], who experimentally studied monoporous and biporous wicks. They found that the 60 μm Cu particles have a distinct performance characteristic in monoporous wicks when compared with other size particles, and the 302/58, 302/72 copper cluster-to-particle ratios had the lowest wall superheat under the same heat flux in biporous wicks. The concept of the hybrid wick was reported by Reilly and Catton in Ref. [14], but no test results were publicly reported. In the current work, the hybrid wick was designed as a 300 μm thick monoporous layer attached to the Cu substrate with a 1200 μm thick biporous layer on top for a total wick thickness of 1500 μm (same as the monoporous standard product). The overall size of each vapor chamber is 107 mm × 99 mm × 5.5 mm with a 1 mm thick Cu substrate thickness, leaving a 0.5 mm thick remaining vapor space.

The scanning electron microscope (SEM) images of the monoporous wick and biporous wick are shown in Figs. 4(a) and 4(b), respectively, each at 150 times magnification. It was confirmed by measurement that the monoporous wick has final sintered particles in the range of 60–100 μm size as expected, with some particle deformation due to the sintering process. From the SEM image of biporous wick, clusters of ∼300 μm size were observed and larger pores between these clusters were visualized, as well. Qualitatively, due to the existence of these larger pores, the biporous wick has relatively larger porosity compared to the monoporous wick of the same particle size. This is further qualitatively confirmed from the SEM images of each wick at a lower magnification (50 times); see Fig. 5.

These larger pores in the biporous wick are expected to provide for good vapor escape, while the clusters are anticipated to provide adequate liquid supply. However, these larger pores may also lead to larger wall superheat when compared to the performance of a monoporous wick, as seen in Table 1 [9]. Therefore, adding a monoporous layer between the biporous wick layer and the Cu substrate should counterbalance the negative effect of the biporous wick, while exploiting its advantages of easy vapor flow and good liquid supply.

Experimental Setup

Heater Design.

The interest of the current work is to evaluate the performance of the three described TGPs at a large heat flux (up to 1 kW/cm2) applied over a large heating area (1 cm2). Therefore, at the center of each TGP, a 10 mm × 10 mm commercial film heater (Mesoscribe™, Cental Islip, NY [19]) with an embedded K-type thermocouple (TC) is printed directly on the center of the Cu substrate with high-temperature solder for the electrical wire connections, as shown in Fig. 6.

The heater is nominally capable of supplying ∼500 W of power (500 W/cm2 heat flux) per the manufacturer specifications with possibility of reaching a 1000 W/cm2 heat flux. To confirm if the heater has the capability to supply higher amounts of power during the TGP thermal performance testing, a pretest of heater performance is carried out using a liquid-cooled test setup. In experimental setup shown in Fig. 7, a Cu substrate of the same footprint area size as the TGPs is clamped between a cold plate and an aluminum (Al) frame. The heater is installed at the center of the Cu substrate. A chiller is connected to the cold plate and the inlet temperature of the circulated water–ethylene glycol coolant is set to 5 °C. A calibrated thermal camera, FLIR SC7650 (accuracy ±1 °C and pixel resolution 640 × 512), is positioned over the top of the heater, Cu substrate, and Al frame. On the upper surface area of the Al frame (including the exposed portion of the heater plus Cu substrate), a 50 mm × 50 mm area is uniformly coated with flat black paint for accurate temperature measurement by infrared (IR) camera. The power supplied to the heater is increased upward from 100 W to confirm the maximum heat flux capability. Each power level is maintained until the temperature reaches steady-state. The heater temperature reading from the embedded TC is monitored by a data acquisition system.

As shown in Fig. 7, there is no temperature fluctuation as the heater power input level is increased from 100 W to 500 W, which indicates that the heater is operationally stable. However, as the heat flux passed the 500 W/cm2 threshold, i.e., at 622.5 W/cm2, the heater temperature did not reach steady-state and continuously increased. When the power input reached ∼700 W, the heater temperature increased at a faster rate making it difficult to control and thus ending the experiment.

In addition to measuring the heater temperature via the embedded TC, the heater temperature was also monitored by the IR camera. It was found that, at 500 W/cm2 heat flux, the maximum temperature within a peripheral portion of the scribed heater trace had already exceeded 300 °C, while the center TC reading was only at ∼140 °C indicating a nonuniform distribution of the applied heat flux. This was not unexpected considering the intrinsic characteristics of the serpentine shaped heater design. At even higher heat flux, it is plausible that hot spots within the heater serpentine trace had a temperature approaching or even exceeding the maximum allowable temperature of the heater of 500 °C. Due to a limitation on the calibrated temperature range of the IR camera, any temperature higher than 400 °C could not be adequately resolved, which is another reason that the heater evaluation test was concluded at 700 W/cm2.

Test Setup.

An air jet impingement test setup is constructed for the vapor chamber thermal performance evaluation test, as shown in Fig. 8. A regenerative blower (Airtech PB1300, Rutherford, NJ) with speed control supplies pressurized air that is passed through two flowmeters (King instrument 7510/7511 Series, Garden Grove, CA), which are arranged in parallel with ranges of 0 ∼ 20 CFM and 0 ∼ 40 CFM, respectively. As shown in Fig. 8, after arriving at the inlet manifold section, the air flows through a series of air straighteners to reduce turbulence. A calibrated K-type TC (±2.2 °C) is mounted in-line with the jet orifice to measure the inlet air temperature. Cool air flows through the 38.1 mm diameter (d) circular orifice and reaches the main test-section, which is fixed on an adjustable positioning stand; refer to Ref. [20] for additional details. In the main test-section, the vapor chamber sample is sandwiched between a straight pin-fin Al heat sink and a polyetheretherketone (PEEK) cap for minimizing heat loss from the evaporator side to the surrounding environment. The heat sink has a 30 × 30 array of 2 mm × 2 mm square pin fins. The fin height is 34 mm, and the fin pitch is 4 mm. Stainless steel bolts are used for clamping the overall stack-up. A 0.5 mm thick graphite thermal pad is placed between vapor chamber condenser side upper surface and the heat sink to reduce the interfacial thermal resistance. A preliminary test is performed to study the effect of the height between the jet orifice and the heat sink fin top surface on cooling performance. The height is tuned from 2.5 cm to 20 cm with a power input up to 60 W. It was found that the TGP effective thermal resistance is nearly independent of the height, H, between the jet orifice and heat sink, which is expected. However, this distance affects the heater temperature due to height dependency of the air side heat transfer coefficient for jet impingement. While the H/d value may logically be further tuned for maximum air side heat transfer, for simplicity, a H/d = 0.33 value was selected based on the prior study [20].

Five calibrated K-type thermocouples (±0.5 K accuracy) are attached on the TGP condenser side surface, see Fig. 8, with four TCs on the four corners, Tb1 ∼ Tb4, and one at the center, Tc. The evaporator side center temperature, Th, is measured using the embedded heater TC. Aluminum tape is applied to affix the thermocouples and overlapped by another thin layer of thermal insulation tape to ensure that the TC readings represent local TGP temperatures. The overall thermal resistance of the TGP is calculated as 
Rtot=ThTwQhQloss=Th(Tc+Tb1+Tb2+Tb3+Tb4)/5QhQloss
(1)
where Tw is the average temperature of the condenser wall, Qh is the heater input power, and Qloss is the system heat loss. Note that the heater input power is directly obtained from the DC power supply via the measured current and a remote-sense line connection that is used to accurately measure the heater voltage drop (to within 1%) directly.

For the current test setup, the bottom side of the heater is insulated by 6.35 mm thick low thermal conductivity, 0.25 W/(m K), PEEK material, while the top side of the heater is a highly thermally conducting TGP plus heat sink. A steady-state conduction-based finite element model of heat loss was developed, where the 100 mm × 100 mm × 5.5 mm TGP was modeled to be a high thermal conductivity, 5000 W/(m K), material. A 1 kW/cm2 heat flux was applied to the 10 mm × 10 mm heated area, and the PEEK insulation material was modeled on the lower surface of the spreader. A representative, 500 W/(m2 K), heat transfer coefficient for air jet impingement was applied to the top surface of the TGP, while a free convection heat transfer coefficient, 2 W/(m2 K), was applied to the exterior surfaces of the PEEK insulation. A mesh refinement study resulted in the use of 2.37 × 105 tetrahedral elements for the analysis domain. Based on this numerical analysis, more than 99% of the applied heat flows upward through the TGP plus heat sink and into the environment. Considering that the system utilizes external air convective cooling, nearly all the heat lost through the heat sink (either by free or forced convection) is logically carried away by the coolant, air. Therefore, in the current work, Qloss was assumed to be negligible, and the total power input was effectively counted toward heating.

Results and Discussion

The experiments were carried out starting from low power with an increment of approximately 10∼20 W until wick dry out occurred. The inlet air temperature was a stable 30.5 °C during testing. The influence of the air volumetric flow rate on the TGP thermal resistance was explored by changing the flow rate from 15.0 CFM to 31.5 CFM under different heater power levels. Although the TGP evaporator side temperature is lower at large air flow rate due to better heat dissipation, the TGP thermal resistance is independent of the air flow rate. This behavior is analogous to the independency of the thermal resistance in relation to varying the H/d value. Therefore, the inlet air flow rate was maximized at 31.5 CFM and kept constant for the experiments. Experiments were carried out multiple times to establish repeatability with no found degradation in performance over repeated tests.

Figure 9(a) shows the heater temperature as a function of time as the heat input is gradually increased from 20 W to 450 W for the biporous wick TGP. Figure 9(b) provides schematics that describe the heat transfer operational stages within the biporous wick. At an early stage, the heat is mainly transferred by evaporation. The boiling incipience started at a power input of ∼60 W, when Th suddenly drops, as shown in Fig. 9(a). This temperature drop is an indication of boiling onset in the wick [21]. Phase change during nucleate boiling absorbs considerable heat, which leads to a sudden drop of evaporator side temperature at the same power input level. As the power level is increased, the TGP operates stably within the boiling stage until the heat flux reaches ∼420 W/cm2. At this point, dry out occurs, which is indicated by the dramatic increase in heater temperature; see Fig. 9(a). At this high-power level, the boiling is so severe that the capillary force provided by the wick cannot supply enough liquid to balance with the vaporization process. At the end of the test, the TGP vapor chamber physically deformed due to overheating and excessive inner vapor pressure at the high power input. The temperature profile of the monoporous wick TGP and hybrid wick TGP followed a similar trend to that shown for the biporous wick TGP in Fig. 9(a).

Figure 10 shows the thermal resistance of the three different TGPs as a function of applied heat flux. All three types of TGPs started with a high thermal resistance at low heat flux, and the thermal resistance gradually decreased as the heat flux increased. When the applied heat flux reached ∼60 W/cm2, there was a sudden drop of thermal resistance for the TGPs with monoporous wick and biporous wick, again due to the onset of boiling in each vapor chamber. The heat flux value at which this sudden drop was observed for the TGP with hybrid wick was around 70 W/cm2 indicating that the hybrid wick produced a delayed onset of boiling. After the boiling onset, the thermal resistance of the hybrid wick TGP decreased more gradually until reaching an approximately constant value after passing 200 W/cm2.

Observe that the commercial monoporous wick TGP exhibits the highest thermal resistance, 0.21 K/W at a heat flux higher than 200 W/cm2, followed by the biporous wicked TGP, 0.18 K/W. The TGP with hybrid wick displays an even lower thermal resistance, 0.15 K/W, which represents an approximate 28% decrease in thermal resistance when compared with the commercial monoporous TGP. Additionally, the dry-out heat flux of the three TGPs is also different at 360 W/cm2, 420 W/cm2, and 450 W/cm2, respectively, for the monoporous wick, biporous wick, and hybrid wick TGPs.

Figure 11 shows the relationship between the heat flux and the temperature differential across each vapor chamber TGP, ThTw. Each curve can be divided into three sections. The switch from the first section to the second section occurs around a ∼20 °C TGP temperature differential for mono/biporous TGPs, while the switch for hybrid wicked TGP takes place at a temperature differential of ∼40 °C. This is due to the delayed boiling onset as discussed in relationship to Fig. 10. There is limited fundamental understanding and experimental evidence of the factors that influence the onset of boiling in vapor chambers. Weibel et al. [22] found that carbon nanotube coatings clearly have the ability to reduce the incipience superheat, although the exact mechanism is not known. This demonstrates that different wick designs can indeed have a significant effect on the behavior.

The superheat at which incipience occurs during capillary-fed conditions can be very high, much higher than is observed in pool boiling. One theory is that there is a sharp temperature gradient in the thin liquid films formed in the wick that increases the required surface superheat per Hsu's seminal theory for bubble nucleation [23]. This is analogous to the increase in wall superheat required for incipience during flow boiling, due to the thinned boundary layer. We speculate that nucleation can be delayed by any structures that promote a thin liquid film near the heated surface during evaporation, based on a body of evidence in the literature on this topic. It is consistent that the hybrid wick structure, with the thin base layer of particles, might increase the superheat required for incipience.

The curves in Fig. 11 have a steeper slope in the second section when compared to the first section due to different heat transfer mechanisms (i.e., boiling for section two but evaporation for section one) as discussed in relationship to Fig. 9. In the stable boiling range, at the same heat flux, the hybrid wick produces the lowest temperature differential. The biporous wick TGP then follows, and the monoporous wick leads to the highest temperature differential. This trend mirrors the thermal resistance order of the three TGPs. Once critical heat flux is reached, the dry out of the wick occurs, which is seen in the sudden increase of the temperature difference for each TGP in Fig. 11.

Based on the experimental results, there are four main findings:

  • (1)

    Within the monoporous wick, liquid supply and vapor escape shares the same flow path, which leads to early dry out.

  • (2)

    The biporous wick separates the liquid supply from the vapor flow which delays dry out.

  • (3)

    The hybrid wick is a two-level wick structure. The thin monoporous wick layer ensures a relatively low boiling thermal resistance, while the top biporous wick provides dual functions (liquid supply and vapor escape) leading to further delayed dry out.

  • (4)

    The vapor chamber with hybrid wick shows that delayed onset of boiling possibly due to the thin base layer of particles promotes a thin liquid film near the heated surface during evaporation.

Although the hybrid wick demonstrated improved thermal performance, lower thermal resistance, and delayed dry out, there is still room for improvement. One example is to use a thicker wick top layer to further increase the liquid supply capability. However, a thicker top layer will increase the wick thermal resistance and make vapor escape more difficult. One way around this issue is to decouple the two layers of the hybrid wick. The benefit is that the monoporous wick layer may be thinner to further decrease the thermal resistance, and the top layer may be thicker for better liquid supply. Then, to overcome the disadvantage of a thick liquid supply layer for vapor escape, artificial vapor vents may be constructed. Putting the above thinking into schematic form leads to a TGP evaporator wick design as shown in Fig. 12, which highlights a three-dimensional drawing of a proposed two-layer wick structure adapted from Ref. [24]. The condensed working fluid returns to this evaporator region from the periphery of the vapor chamber through a conventional bulk wick. Liquid is routed from the bulk wick surrounding the evaporator section into a relatively thick wick cap layer into an array of vertical liquid-feeding posts. These posts uniformly distribute the liquid to a thin base wick. Vapor generated by capillary-fed boiling in the base wick escapes through gaps between the posts and travels through vapor vents in the cap wick layer into the vapor core.

Conclusions

In summary, TGPs with a biporous wick and hybrid wick were designed and fabricated based on wick level test data reported in the open literature. The two TGPs were compared with a commercial monoporous wick TGP from the perspectives of thermal resistance, boiling onset, and dry out heat flux. The two-layer wick structure of hybrid wick demonstrated the lowest thermal resistance, delayed boiling onset, and higher dry out heat flux. However, it is postulated that the intrinsic shortcomings of a monolithic hybrid two-layer wick limit its further performance improvement. Based on a similar idea, which in short leverages the separation of the local liquid supply path from the vapor flow path and utilizes a thinner base wick plus thicker top layer, a novel two-layer wick is targeted for future development. Following Ref. [24], the next step is to optimize the structure of the two-layer wick and apply it to a vapor chamber TGP. The performance of the TGP will be evaluated in a similar fashion to demonstrate its capability in spreading 1 kW/cm2 from a 10 mm × 10 mm heated area to a two-order of magnitude lower heat flux level for synergy with forced air cooling.

Acknowledgment

The authors thank Purdue University, specifically Dr. Justin Weibel, Mr. Srivathsan Sudhakar, and Dr. Suresh V. Garimella, for their technical discussions and ongoing collaboration related to this work.

Nomenclature

     
  • d =

    diameter of jet orifice, m

  •  
  • H =

    distance between jet orifice and heat sink, m

  •  
  • Q =

    power, W

  •  
  • R =

    thermal resistance, K/W

  •  
  • T =

    temperature, °C

Subscripts

    Subscripts
     
  • b =

    boundary

  •  
  • c =

    center

  •  
  • h =

    heater

  •  
  • loss =

    heat loss

  •  
  • P =

    power supply

  •  
  • tot =

    total

  •  
  • w =

    condenser side surface wall

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